A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning

arXiv:2609.17804 · cs.AI, cs.LG · Submitted 2026-09-15 · Read on arXiv

cs.AI, cs.LG

Submitted: 2026-09-15

Updated: 2026-09-15

Code: https://github.com/deliaqu/llm-reasoning-decomposed

License: http://creativecommons.org/licenses/by/4.0/

The gist: Large language models solve grade-school math word problems with high accuracy, yet a single irrelevant clause inserted into the problem can collapse it.

Terminology

Abstract

Large language models solve grade-school math word problems with high accuracy, yet a single irrelevant clause inserted into the problem can collapse it. We reconcile these observations with a mechanistic account. We show that the model's internal computation decomposes into a four-stage sequential pipeline, Schema Abstraction, Operation Planning, Operand Binding, and Computation, each stage producing a distinct intermediate representation in an identifiable band of layers. Using the same scaffold to diagnose distractor-induced failure, we localize the corruption to a single stage, Operation Planning, implemented by a set of attention heads whose causal role we validate bidirectionally. In short, we provide a mechanistic interpretation of math word problem reasoning in LLMs, and their failure when distracted.

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